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(a) If P and Q are both false, then ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) is true. If either P or Q are true, then ¬((¬P → ¬Q) ∧ (¬Q → R)) is false. (b) If P and Q are both true, then ¬((¬P → ¬Q) ∧ (¬Q → R)) is true. If either P or Q are false, then ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) is false.

(a) Not ((¬P ∧ Q) ∨ ¬(R ∨ ¬S))

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Question: Use DeMorgan’s Laws, and any other logical equivalence facts you know to simplify the following statements. It would be a good idea to use only conjunctions, disjunctions, and negations. (a) ¬((¬P ∧ Q) ∨ ¬(R ∨ ¬S)) (b) ¬((¬P → ¬Q) ∧ (¬Q → R))

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(a) (P ∨ ¬Q) ∧ (R ∧ S) (b) (P ∧ Q) ∨ (Q ∧ ¬R)

Answered by text-davinci-003

Jan. 29, 2023, 4:20 p.m.

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This article was generated in part by one of OpenAI’s large-scale language-generation model, answering user cassidipark's question. Images were generated with OpenAI's AI model, DALL·E 2. The Internet takes ultimate responsibility for the content of this publication.
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Published: Sunday, January 29, 2023

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